item 20: gate threshold curve + oracle bound (probs pass, merge per-item LUT, offline sweep)

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

results-loop/PROTOCOL_UNIFIED.md

@@ -439,3 +439,18 @@ and compute savings are demonstrated and cheap; difficulty-selective
 DEPTH allocation remains unsolved at 3K-param-head scale — binding
 constraint is classifier quality on the k=0/s0 state, exactly where E0
 started. Next per plan: threshold sweep (cheap) before any E2.
+
+20. **E1 threshold curve + oracle bound (pre-registered 2026-07-16 ~02:15,
+    before running).** Phase 1: record E1c head's halt probabilities per
+    test item (one GPU pass). Phase 2: per-item outcomes for the frozen
+    curriculum merge at k=0/1/2/4 (four generation sweeps, tag merge_lut —
+    doubles as the reusable gate-evaluation lookup table and supplies the
+    long-missing per-item logs for the canonical merge). Phase 3 (offline):
+    gated accuracy at thresholds .3-.99 by composing k*(theta) with the
+    lookup; plus the ORACLE gate (best k per item) = the ceiling any gate
+    can reach with this merge. Predictions: (a) some theta gives hard >=
+    32% with easy >= 93% and E[k] <= 2.2 (dominating E0 on compute at
+    comparable accuracy); (b) the curve is monotone in theta; (c) oracle
+    overall >= 55% — if so, gate-quality headroom is large and further
+    gate work is justified; if oracle < 53%, gating this merge is nearly
+    saturated and the program pivots to E2 or closes.